On monoidal equivalences and Ann-equivalences

TL;DR

This paper presents a new proof of categorical equivalences using a strict monoidal category construction, with applications to Ann-categories and almost strict Ann-categories.

Contribution

It introduces a novel proof technique for monoidal and Ann-category equivalences based on a strict monoidal category framework.

Findings

Constructed a strict monoidal category M(C) of M-functors and M-morphisms.

Proved the equivalence of category C to M(C).

Applied techniques to establish equivalence between Ann-category and almost strict Ann-category.

Abstract

In this paper, we show another proof of the problem by constructing a strict monoidal category M(C) consisting of M-functors and M-morphisms of a category C and we prove C is equivalent to it. The proof is based on a basic character of monoidal equivalences. Ideas and techniques of these proofs can been used to prove the equivalence between an Ann-category and an almost strict Ann-category.